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Roche volume filling of star clusters in the Milky Way
Andreas Ernst, ARI Heidelberg
Aarseth N-body Meeting 2012Bonn, Dec. 3-5, 2012
Outline
Roche volume – what is it? Roche volume filling Resonances, Periodic orbits N-body simulation van den Bergh correlation Analysis of existing data sets Results
Questions / Thoughts● To what extent do open and globular clusters fill
the Roche volume?● What is the difference between open and
globular clusters with respect to Roche volume filling?
● Jacobi radius provides a natural scale● Another scale is given by the position/width of
the main resonant island
Van den Bergh (1994) Slope 2/3≃
Correlationcoefficients:
0.85 [Fe/H]<-2.00.60 -2.0<[Fe/H]<-1.00.42 [Fe/H]>-1.0
Van den Bergh correlation
Jacobi radius (King, 1962):
r J3=
GM cl
2−d 2dR2
Distance of the cluster center to theLagrange points L1 and L2
, : angular velocity, gravitational potential of the galaxy
Van den Bergh correlation
=V C2 ln RR0
ddR
=V C
2
R
d 2dR2 =−
V C2
R2
2=L2
R4
L=?
Isothermal sphere:
Van den Bergh correlation
L=V C RP RA 2 ln RA /RPRA
2−RP2
Isothermal sphere:
Angular momentum of an orbit as a function of peri- and apocenter
Van den Bergh correlation
r J3=
GM cl RA2−RP
2 R4
2VC2 RP
2 RA2 ln RA /RPV C
2 RA2−RP
2 R2
Define guiding radiusRg=LV C
r J=GM cl
V C2
1 /3
R4
Rg2R2
1/3
Jacobi radius
Van den Bergh correlation
Van den Bergh (1994, 2011)rh∝RGC
2 /3
Jacobi radius in an isothermal halo:r J∝RGC
2 /3 for RGC≫L /V CThese proportionalities and the assumptionof an isothermal halo imply that
rhr J
is independent ofRGC
for Milky Way GCs within the scatter of the correlation.
The ratio rh/r
J
r J=[ GM cl
4−22 ]1 /3
, =, M cl=
83
rh3
for OCs: rhr J=[ 34−22
4G ]1 /3
= 4−2
2 1 /3
torbT orb 2 /3
for GCs: rhr J t
= t orb2 2/3V C22
1 /3
Rg2R t 2
Rt 4 2 /3
Values for GCs and OCs
Samples by Piskunov et al. (2007), Dinescu et al. (1999), Harris (1996, 2010 edition)
rh/r
J and r
t/r
J for GCs and OCs
- Two distinct populations with respect to r
h/r
J
- rh/r
J of OCs is
larger
- OCs: King W
0=2-3
- GCs: King W
0=5-6
rh/r
J and r
t/r
J for GCs and OCs
Ernst & Just, submitted (2012)
rh,2D
= projected half-mass radius (OCs) or half-light radius (GCs)
Conclusions GCs are presently Roche volume underfilling In the pericenters of their orbits they might be Roche
volume filling or even Roche volume overfilling Assumptions:
– GCs have approx. constant angular momentumin an purely isothermal halo
– Disk/Bulge contribution can be neglected
Thank you for your attention!